Morphological scale space and mathematical morphology

Abstract

It is well known that a conveniently rescaled iterated convolution of a linear positive kernel converges to a Gaussian. Therefore, all iterative linear smoothing methods of a signal or an image boils down to the application to the signal of the Heat Equation. In this survey, we explain how a similar analysis can be performed for image iterative smoothing by contrast invariant monotone operators. In particular, we prove that all iterated affine and contrast invariant monotone operators are equivalent to the unique affine invariant curvature motion. We also prove that under very broad conditions, weighted median filters are equivalent to the Mean Curvature Motion Equation.